Electrical – Neutral on main service breaker

Turn off all loads on the circuits in question.

Turn off the main for this panel. Possibly overcautious, but that's part of what's let me get old.

Either: short the dead circuit, or turn on an incandescent bulb on it (main off, circuit dead, still dead - just the bulb/fixture/lamp turned on.)

Pull neutrals and look for one with low resistance from the hot in question. There should be only one. Unshort the circuit or turn off the lamp and make sure the resistance changes (if nothing else is turned on, should be infinite, but if there are things that are not able to be switched off, may be non-infinite. But you should see a difference when you switch the incandescent lamp off or remove the short - it's a form of verification.

I think you have enough neutrals not to worry too much about this, but: beware of "Multi-Wire-Branch Circuits" where one neutral serves two hots.

As for the wire colors, only white and green (with or without yellow stripe) are reserved (and IIRC, you can retag white to another color, but you can't retag green - and you can't retag anything else to white.) If your wiring is run in conduit, using the full range of available colors makes figuring out (what is connected to) the hot side of circuits much, much easier. Most household wiring is not run in conduit, so it's not often seen at home.

Up until 2011 the National Electrical Code allowed a "3 wire" method of connecting a sub-panel. This means you have the two "hot" wires and a neutral running to the sub-panel as opposed to the "4 wire" method where you add a separate equipment ground wire.

So, when your house was built, it was perfectly legal to use the 3 wire method. There is no problem with this unless you connect a metal pathway, such as a water pipe, from one building to the other. This allows neutral current to flow on this parallel path. This could be potentially lethal to someone working on the pipe.

As to the main panel not having a neutral: it does. If you look again you will see the two hot wires and a bare conductor. There is no ground wire on the service drop. The bare conductor is the neutral. This is allowed on the service drop, but from that point on all neutral conductors must be insulated. Ground wires are always allowed to be bare.

So, in short, there is no problem with your system unless you run a metallic system to the sub-panel building. This would create a problem.